On the steady-state propagation of an anti-plane shear crack in an infinite general linearly viscoelastic body

Author:
Jay R. Walton

Journal:
Quart. Appl. Math. **40** (1982), 37-52

MSC:
Primary 73M05; Secondary 73F99

DOI:
https://doi.org/10.1090/qam/652048

MathSciNet review:
652048

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Abstract: The steady-state propagation of a semi-infinite anti-plane shear crack is considered for a general infinite homogeneous and isotropic linearly viscoelastic body. Inertial terms are retained and the only restrictions placed on the shear modulus are that it be positive, continuous, decreasing and convex. For a given integrable distribution of shearing tractions travelling with the crack, a simple closed-form solution is obtained for the stress intensity factor and for the entire stress field ahead of and in the plane of the advancing crack. As was observed previously for the standard linear solid, the separate considerations of two distinct cases, defined by parameters and , arises naturally in the analysis. Specifically, and denote the elastic shear wave speeds corresponding to zero and infinite time, and the two cases are (1) and (2) , where is the speed of propagation of the crack. For case (1) it is shown that the stress field is the same as in the corresponding elastic problem and is hence independent of and all material properties, whereas, for case (2) the stress field depends on both and material properties. This dependence is shown to be of a very elementary form even for a general viscoelastic shear modulus.

**[1]**C. Atkinson,*A note on some dynamic crack problems in linear viscoelasticity*, Arch. Mech. (Arch. Mech. Stos.)**31**(1979), no. 6, 829–849 (English, with Russian and Polish summaries). MR**583773****[2]**C. Atkinson and C. J. Coleman, J. Inst. Maths. Applics.**20**, 85-106 (1977)**[3]**C. Atkinson and C. H. Popelar,*Antiplane dynamic crack propagation in a viscoelastic layer*, J. Mech. Solids**27**, 431-439 (1979)**[4]**F. D. Gakhov,*Boundary value problems*, Translation edited by I. N. Sneddon, Pergamon Press, Oxford-New York-Paris; Addison-Wesley Publishing Co., Inc., Reading, Mass.-London, 1966. MR**0198152****[5]**J. R. Willis,*Crack propagation in viscoelastic media*, J. Mech. Phys. Solids**15**, 229-240 (1967)

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DOI:
https://doi.org/10.1090/qam/652048

Article copyright:
© Copyright 1982
American Mathematical Society